The centre-back moved to Old Trafford from Spartak Moscow in 2006 and has won five Premier League titles and the Champions League with the Red Devils.
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"It's the last year of my contract and I have had eight wonderful years here. My time at this great club will always rank as the best years of my career," he said in a statement to the club's official website.
"I never could have imagined winning 15 trophies and I will certainly never forget that fantastic night in Moscow, memories that will live with me and the fans forever.
"However, I have decided that I will move on at the end of this season. I want to challenge myself again and try to make the best of myself in the coming years.
"I’m not considering staying in England as the only club I ever wanted to play for here is Manchester United and I was lucky enough to be part of this club for so many years. I’ve got a few options to move on and I will choose the right one for me and for my family.
"I am now going to focus all my efforts on playing for Manchester United and do the best I can for the team until the end of the season. I hope this stops any further speculation about my future."